Asked by Dheandra Armyra on Jun 28, 2024
Verified
A firm's total cost function is given by the equation:
TC = 4000 + 5Q + 10Q2.
(1) Write an expression for each of the following cost concepts:
a. Total Fixed Cost
b. Average Fixed Cost
c. Total Variable Cost
d. Average Variable Cost
e. Average Total Cost
f. Marginal Cost
(2) Determine the quantity that minimizes average total cost. Demonstrate that the predicted relationship between marginal cost and average cost holds.
Total Cost Function
A mathematical representation of the total economic cost of production, which includes both fixed and variable costs, as a function of output level.
Fixed Cost
An expense that remains constant regardless of the volume of products or services produced or sold.
Variable Cost
Expenses that directly fluctuate in relation to the amount of goods or services produced, including labor and materials.
- Gain knowledge of and execute applications of cost theories, including variable, fixed, marginal, average, and both average variable and fixed costs.
- Examine how marginal cost interacts with different average costs (total, variable, fixed) in the context of cost behavior.
- Compute and elucidate cost functions, comprising total cost, average cost, and marginal cost, utilizing given data or formulations.
Verified Answer
ZK
Zybrea KnightJul 04, 2024
Final Answer :
PART (1)
a.TFC = 4000
b.AFC =
c.TVC = TC - TFC
TVC = 5Q + 10
d.AVC = 
= 
= 5 + 10Q
e.ATC =
= 
f.MC = 5 + 20Q
PART (2)
ATC is minimized where MC is equal to ATc.Equating MC to ATC
= 5 + 20Q
4000 +5Q +
= 5Q + 20 
4000 = 10 
= 400
Q = 20
ATC is minimized at 20 units of output. Up to 20, ATC falls, while beyond 20 ATC rises.
MC should be less than ATC for any quantity less than 20.
For example, let Q = 10:
MC = 5 + 20(10) = 205
ATC =
= 505
MC is indeed less than ATC for quantities smaller than 20.
MC should exceed ATC for any quantity greater than 20.
For example, let Q = 25:
MC = 5 + 20(25) = 505
ATC =
= 415
MC is indeed greater than ATC for quantities greater than 20.
a.TFC = 4000
b.AFC =
c.TVC = TC - TFCTVC = 5Q + 10
d.AVC = = = 5 + 10Qe.ATC =
= f.MC = 5 + 20QPART (2)
ATC is minimized where MC is equal to ATc.Equating MC to ATC
= 5 + 20Q4000 +5Q +
= 5Q + 20 4000 = 10 = 400Q = 20
ATC is minimized at 20 units of output. Up to 20, ATC falls, while beyond 20 ATC rises.
MC should be less than ATC for any quantity less than 20.
For example, let Q = 10:
MC = 5 + 20(10) = 205
ATC =
= 505MC is indeed less than ATC for quantities smaller than 20.
MC should exceed ATC for any quantity greater than 20.
For example, let Q = 25:
MC = 5 + 20(25) = 505
ATC =
= 415MC is indeed greater than ATC for quantities greater than 20.
Learning Objectives
- Gain knowledge of and execute applications of cost theories, including variable, fixed, marginal, average, and both average variable and fixed costs.
- Examine how marginal cost interacts with different average costs (total, variable, fixed) in the context of cost behavior.
- Compute and elucidate cost functions, comprising total cost, average cost, and marginal cost, utilizing given data or formulations.